Examining the Population-Structure Models Used in NAEP

The population-structure models are examined in two ways. First, the proportion of variance accounted for by the principal components is provided for each contrast of the group-defining variables. When these values are close to one, most of the variability in the group-defining variable is accounted for by the principal components used in the population-structure model, and the population-structure model reflects membership in the group well.

Second, the proportion of scale score variance accounted for by the population-structure models is provided for each sample. These values report the proportion of variance among scale scores explained by group membership for each sample. When these values are larger than zero, the population-structure model is needed to estimate summary statistics for the population and student groups represented by the sample.